Without getting into the subject of when to use very soft materials like schlappen...
Plain old Rit black, by itself, will get you very close to what you want. Leave it in the dye until you get the darkness you desire.
Years ago I read a piece by a famous fly tier--perhaps Polly Rosborough?--that to get a true black with Rit you needed to add some Rit brown to the black. It's true. With plain Rit black you get a bluish cast--a pretty nice dun.
I haven't tried dying schlappen, but this approach has worked very well with dry fly hackle.